I want to teach the new charizard I'm training Solarbeam but I already used the tm on another charizard. Is there still a way to teach it Solarbeam or am I never going to be able to teach a charizard Solarbeam again?

Starting in Generation 5, all tms and hms can be used a infinite number of times. So, You already thought the old Charzard solarbeam but you can teach the new one solarbeam too. So, you can teach this new charizard solarbeam and other Pokemon that can learn solarbeam and you can reuse the Tm an infinite number of times.